A micro optofluidic lens is formed by laminar streams of immiscible liquids with different refractive indices. This paper reports modelling and characterization for a new design of a micro optofluidic lens. The lens has a circular chamber allowing the formation of interfaces with a perfect arc shape. The inlet and the outlet of the lens chamber are placed with an offset to the chamber axis to achieve a radius of curvature smaller than the limiting chamber radius. A model mathematically predicts the relationship between the flow rate ratio and the curvature of the interface and the resulting focal length. The device was fabricated and tested with laser light guided by optical fibres. Experiments were carried out to verify the analytical model. Benzyl alcohol and ethylene glycol were used as optical media to form the lens. Due to the small radius of curvature, better focusing ability than the previous symmetric design was achieved. On-chip focusing with fibre-to-fibre transmission was demonstrated with this micro optofluidic lens.